No, network consensus, i.e., almost all the nodes on the network are ready to accept a new version of blocks.
Are we talking about clients, relays or miners ?
Everyone running a node that retrieves a full copy of blockchain, so all of them except SPV clients.
So relays it is.
I will tell you now how to reach hard-fork "consensus" using relays.
1. Make all relays (or let's assume 75% of relays) upgrade to the Bitcoin Classic
2. The old software that the relays are not using becomes irrelevant
3. Miners, seeing that they are mining using outdated software (and thus are/will be on the wrong chain) quickly upgrade their software to Bitcoin Classic, because otherwise they would lose all profits.
4. Big payment operators, seeing what is happening, also quickly upgrade their software to Bitcoin Classic
All happens within days, if not hours.
5. All the rest of the network (laggards) upgrades to Bitcoin Classic (this may take little longer time)
Boom ! Consensus reached, baby.
Also note that the money left on the old version aren't lost. Users just need to upgrade to use them.